Peschanenko V. Methods of Computer Algebra and Symbolic Conversion at the Design of Mathematical Systems of Educational Purpose

The methods of construction of many-sorted algebras in structure terms of extensions, homomorphisms, isomorphisms and inheritance of many-sorted algebras are developed in this dissertation. It is built the mathematical model of algebraic calculations module of mathematical system of education purpose in terms of extensions, homomorphisms, isomorphisms and inheritance of many-sorted algebras of TerM system. Herein it was realized the mathematical model of algebraic calculations module TerM in view of prototype and final version in the system of algebraic programming APS. In the present work it is determined the system and technological requirements to the systems of algebraic calculations design. The algebraic programming system APS was brought in conformity with these requirements. Also the methods of insertion programming were applied to the problems of prototyping and realization of many-sorted algebras. It was grounded and realized the specific task generation algorithms and check of step of solvingof algebraic tasks, generation of process of solving of algebraic tasks and other applied tasks in the system of educational purpose TerM. As a result it was built the mathematical system of educational purpose, that supports in complex the learning process of algebra at school.